If you are still wondering, with just a few hours to go before tonight's potentially fascinating final of Euro 2012 between Spain and Italy, it is still possible to walk down the cobbles of the Andriyivskyy Descent without fear of marauding young Fascists.

Along the main artery of Khreshcatyk leading into Freedom Square – reduced by Red Army dynamiters to rubble as the Germans advanced in 1941 – Spanish and Italian fans amiably discuss their prospects.

There is also to be found a small group of English stoics discussing proudly the technique of falling asleep while clutching a glass of beer or wine and then waking up some time later without the spilling of a single drop.

Euro 2012 was billed by some as one of football's ultimate misadventures, bringing to a large, troubled swathe of Eastern Europe the world's second most important tournament.

It was to court sickening extremes of racism and unbridled gouging by hotels, apartment agencies, taxi drivers and restaurants.

Plainly, there have been examples of all of that, with racism in Poland rearing up with sporadic ugliness. But here in Ukraine, where many saw it as a much bigger threat, there has not been a glimmer of the horrors anticipated by the BBC Panorama edition which had graphic footage of some young Ukrainian fans attacking Asian youths at a club game.

However, for a month now the thugs have been in hiding, or maybe sharing the same kind of retirement of those English fans who once tried to wreck a stadium in Dublin while shouting "No surrender to the IRA".

There has been gouging, no doubt, but as the taxi driver who took me on the 35-minute run to the airport the other day for the equivalent of £12 said: "When people can hardly live, when five per cent have the money to pay for houses like that (pointing to a spectacular development on the bank of a wide sweep of the Dnieper River) and the other 95 per cent have nothing, people will try to make the best of any opportunity. It is not greed, it is desperation."

Circumstances will be distinctly different and certainly more comfortable in France in four years when the president of Uefa, Michael Platini, takes home his extended tournament (with 24 nations rather than the old 16 to delight the all-powerful TV schedulers). Yet there has been a persistent, nagging feeling these last few days in this historic city of quite ravishing natural and architectural beauty.

It is that looking back on the tournament that ends at the Olympic Stadium around midnight will, at the very least, carry a degree of ambivalence.

No regrets at leaving behind the Polish banana-throwers, of course, but certainly a belief that the world's most popular game has been fulfilling a function quite separate from the accumulation of vast profits.

It has been touching people, millions of whom do not normally have so much to celebrate beyond that which they can create with their own humanity, in the way that the World Cup did in South Africa two years ago.

That essentially joyous event – for such it was when you could avert your eyes from the cavalcades of Fifa limousines pouring out of Johannesburg's most expensive hotel – was previewed quite as darkly as the one here.

The big alarm then was that the streets would run red with tourist blood, but that didn't seemed to bother the stars of Germany when they adopted the township near to their training centre outside Pretoria – or Diego Maradona when he strolled into another one and was besieged by great throngs of boys and girls.

If football is indeed a universal language, it needs to bring the oxygen of involvement not just to the rich and developed places but somewhere like here where the disparity between the rich and the poor is worn as brazenly as the handguns of some of the diners at the most expensive restaurants.

When national hero Andriy Shevchenko scored his goals against Sweden you were reminded of this as surely as you would have been in the poor districts of Mexico City and Seoul when the World Cup passed by in 1970 and 1986 and 2002. The streets erupted.

Shevchenko later handed a shirt to the six-year-old whose ecstasy had been captured by television. It was an image that reminded you of the young Iraqi celebrating his nation's Asian Cup victory over Saudi Arabia five years ago. The authorities warned fans not to congregate and make themselves targets for the bombers, but for a little while the smiling boy was living in another world.

Here yesterday Platini was unveiling his latest extravagant proposal. It is to make the 2020 tournament a continent-wide project, with teams competing in as many as 13 separate countries. It sounds like another move to put international football in the jet-lane and guarantee the hold of television.

It could mean that there are just a few more hours left to savour another kind of concept – one which takes the game and its uplifting potential to places like Ukraine which are not overstocked with opportunities, to be, however briefly, at the centre of the world or a great continent.

One last and entirely reasonable hunch is that a difficult but essentially successful experience will be crowned by a game to linger in the mind. If Italy win, as is the suspicion here, it will be another reminder of football's genius to surprise. The people of Ukraine will be entitled to share in a little of the glow.